Confused!!

I'd hold the door open for him.

I’d honestly recommend having a conversation when you’re both calm, explaining WHY the routine matters to you, hearing his perspective, and figuring out a routine that works for both of you. You’re both learning how to navigate parenthood, and neither of you should feel like you’re parenting against each other instead of working together.
You also have to remember that Dad needs the opportunity to learn his own way of caring for the baby, too. That doesn’t mean your routines and concerns should be dismissed, but there needs to be room for both of you to grow as parents. The goal isn’t for him to do everything exactly how you do it; it’s for you both to agree on what’s best for your baby and support each other in making that happen.
And please don’t ignore the fact that he’s threatened to move out three times. That’s something that needs to be discussed separately, because disagreements about parenting shouldn’t automatically turn into threats of leaving. You deserve to feel secure!

Honestly it’s really common for disagreeing to happen postpartum. 13 weeks is still so so early . Yall are still adjusting which will take some communication and learning each others parenting styles . No it’s not ok for him to threaten to walk out and storm out during hard conversations. It shows he is afraid of conflict . Until he is actually walking out id continue to keep trying to communicate and be patient. Babies can sense when parents are frustrated it makes things way more stressful

Yes do find a time to talk about it when you guys are doing well and are happy being together. The exhaustion of taking care of a baby and the sleep deprivation I know can make it hard sometimes to find time but part of the exhaustion also can hinder the way you communicate whether you intend it or not. I used to be able to control my tone and temper when having a disagreement with my husband but after the baby it’s much harder to care how I say things because I’m just mentally and physically exhausted and sometimes the way I say things can be harsh even though I didn’t mean for it to so if you could talk to him when u have been well rested and in a good mood instead of in the moment

Keep communicating. It’s likely he is trying in his own way and then to keep getting told (in his eyes!) that he’s doing something wrong can be quite hard. Men are also susceptible to PPD. I’m not saying it’s okay for him to say what he did but also it’s worth considering the bigger picture and context when you’re so early in this journey.

But also for him to say that to you is just mean and uncalled for. Maybe he is also exhausted and unable to think when he speaks to you in the moment. Make it clear that those words really hurt you and that it’s not okay for him to say that regardless of the situation